Trailing by as many as 12 in the first quarter, Germany had drawn level at 36-36 by halftime and after a tense third quarter roared away in the fourth to book a meeting with either host nation France or Canada for a place in the final.
NBA star Antetokounmpo scored 22 points but 18 points in reply from Franz Wagner was enough for Germany to maintain their four-game unbeaten record.
Wagner said the whole German team pulled together to slow Antetokounmpo.
"It was more than half of the scouting report, so a big part of our preparation," he said of the need to contain the Greek superstar.
"It takes all five on the court to try to stop him, but I thought we did a good job, especially in the second half, of at least trying to contain him."
Greece started strongly and Antetokounmpo brought their fans to their feet with a dunk that gave them a 16-4 lead with five minutes remaining in the first quarter.
Nick Calathes found Antetokounmpo for an alley-oop dunk less than a minute later, following up with a three-pointer that gave Greece a 12-point lead with less than a minute left in the first.
But Germany slowly turned the tide, Franz Wagner and Moritz Wagner scoring six first-half points apiece, and tied the scores up at half-time.
Dennis Schroder opened the third with a three-pointer that gave Germany their first lead of the game.
And after a back-and-forth battle, Isaac Bonga's three-pointer at the buzzer to end the third sent the Germans into the final period with a 59-52 lead.
Johannes Thiemann finished with 10 points, six rebounds and a steal and Schroder had 13 points and assists coming off the bench.
"We struggled with their physicality, but I thought our second group came in and did an outstanding job in that end of the first quarter and really kind of gave us the energy and physicality to get back in the game," Germany coach Gordie Herbert said.
"We made a couple of changes with the defensive game plan and that's all we did really."
